Archive for March, 2009

At the cutting edge of mathematics is a function sometimes called “tetration” or “hyperpower” with which you stack exponentials, like 2 to the (2 to the (2 to the 2)), which you can then write as 42. The parentheses are there because you have to do the top power in the stack first. As compared to common functions like exponential or addition it is poorly understood, and we don’t really have a convenient or very much consistent way of finding values for things like ½2. While 2½ is just the number such that when you bring it to the 2nd power you get 2, i.e. (2½)2 = 2, it turns out that 2(½2) is not 2, and there isn’t any easy way of defining the hyperpower function for anything but integer values (that is to say, with f(x) = x2 only letting x be an integer.) You can even go into negative integer values by taking logarithms.

If you have excel, you can type in a simple formula: in cell A1, put a 2, in cell A2, just type in =2^(1/A1), and then do the click-drag trick (click-drag on the little black square in the lower right hand corner of the selected box) to copy the formula into the cells below. You end up with a column of values where each is based on the value of the cell above it. It’s a “recursive” formula, and by the time you get to A60 the value it shows should be something like 1.55961. 1.559611.55961 ≈ 2. Or we can say, 21.55961 approximately equals 2 (“≈” means “approximately equal to,” we have to say “approximately” because there are probably infinitely many digits to this number that starts 1.55961, but 6 of them is enough to make the point I am trying to make.)

Why do I think this is interesting? Because despite the mathematical establishment’s efforts (and there have been a fair bit, just wikipedia “tetration” or go to here) this excel method is probably by far the easiest way to come up with these hyperpower “roots” (to borrow the term.) It doesn’t have quite the rigor or proof of methods like finding a complete summation expansion for the function that could be used with any complex number and to find derivatives and integrals, but there is some basic logic here – if excel was going to come up with a number (and not infinity or zero or some chaotic values), the number it would come up with would be one that satisfies the relation y = x1/y. If x equals yy, this relation is always true.

In essence, what we have done is set a constraint, in the form of this recursive formula, and then let the program run. Excel calculates by using computer code, which is processed by the CPU, which is really just a finely manufactured collection of basic circuit elements like transistors. Physicists can describe very precisely how these basic circuit elements work. In a broad stroke of reductionism, the universe is doing the calculation. We may write the code and design the CPU, but if the way electrons behaved were to change, the computer screen would display different results. If you are one to believe in the material nature of the mind, you might argue that all the calculations that have and will ever be done are actually done through the repetition of events that take place in the physical universe and that we associate with an abstract mathematical process – the universe is doing all our work.

That’s not to say the universe is perfect – quantum mechanics implies a sort of “truth in the limit,” that the average result of an identical event measured an infinite number of times will be a mathematically predictable value. But for any given event there is some degree of stray from this average value. Through the ordered and also inherently random nature of the universe, its components evolve and move towards the stabilities provided by the natural constraints. Just like the numbers in the excel file, which are actually physical processes that we correlate to the abstract theory of mathematics, the particles of the universe interact solely through events that correspond (though not completely) to mathematical entities and reveal the qualities of reality. The anthropic nature of the universe, that we and everything in it exist because of its properties, is the fulcrum of physics. And if you believe in the power of reduction, we exist as the collection of events and changes that arise out of a combination of mathematics and inherent randomness. The various parts of ourselves that comprise any substance or action are a retention of data and the program of natural process that erases part of the data and then conducts an action based on it but it a manner that is obscured from us. We are the likely & stable members that arise from the universal tendency. But we have to hope that we don’t have enough of the story or entropy is conquerable or dark energy doesn’t exist, or else we are only finitely stable.

There are already such things as online book trading and lending communities, but as these rely on the mail, they are not quit effective as libraries.

I propose a localized version of these sites in which:

1) Members sign up and list all of the books they are willing to lend.

2) The listed books are compiled on a searchable database.

3) Local businesses (like coffee shops) act as drop off/pick up hubs. This keeps strangers from being invited to your house.

4) Upon a request, the lender will drop the book off at the public spot within a week. This allows lending to be at the lender’s convenience and to save the cost/hassle of shipping.

5) Borrowers deposit collateral (via internet payments) into a joint bank account that is equal to the value of any books borrowed. This ensures that any lost books can be replaced. Once they return their book, they are refunded.

6) Any interest that accrues will be used to pay for the C.L.’s webspace. Any additional interest will be given to literacy-promoting charities.

7) This system will provide a diverse selection of books, promote literacy, promote local book culture, and create connections of readers and naturally growing networks of people with convergent book interests. It should be minimally expensive to set up and run.

I was invited to participate in a collaborative fiction project in another corner of the internet. Since we here at Ghost Island like collaborative fiction projects, I thought I’d share this one. It’s called ‘For Every Year’ and involves writing a short story for every year since 1400. It has a lot of rad contributors and is run by one Crispin Best. I like it. Maybe some GI people will want to submit?

“I know a mouse, and he hasn’t got a house, I don’t know why he’s called Gerald, He’s getting old, but he’s a mouse.” He kept repeating over and over again, getting less and less coherent each time, occasionally forgetting words, or swapping in new ones that may or may not have fit. Talk singing, not slurring his speech, but not making sense either, no discernible tune. His red polo shirt was not tucked in, no name tag, reddish blond hair not combed or washed, he was not wearing the required all black shoes.

“I think you should go home Ryan.” Said Henry, the obviously closeted Staples manager, mid thirties, poor knock off of a JFK haircut. All before Ryan even had a chance to get out his box cutter and start shelving the merchandise.

“Forever…?” Ryan asked, sounding increasingly more delirious.

“No, just for today Ryan.” Said Henry, without any of the frustration that a retail manager would presumably have, when one of his employees shows up for a shift obviously stoned. I don’t know exactly when this was during my Junior year of high school. But it must have been somewhere towards the end, because I recommended Ryan, my best friend at the time, for the job, somewhere in the later half of my 6 months of employment at the local Staples. My first real job, with a W2, a punch in clock, a cash register, a uniform.

This scene replays in my mind so easily because Gerald bothered me for awhile. Who was Gerald? Is he actually old? Was that from a song, or just rambling? Since when does Ryan hang out with mice? I never got around to asking him about it, probably because I assumed that he wouldn’t remember what he said, just that he was sent home. Or that the stoned rambling of a suburban teenager doesn’t mean anything. But who’s to say? I’ve never smoked. There was something to the simple notion of this mouse, something that stuck with me. Later that year Ryan and his family moved to the Midwest, and out of my life since.

I thought I missed my answer, until the summer after college when I bought some music at the tag sale of a downstairs neighbor I never knew. I didn’t count them, but I would have to guess that there were close to 300 cassette tapes in the collection. Most of them were hand made, hand labeled, hand written. Years of work. He offered me ten dollars, and I gladly accepted. His wife was not pleased, but he could tell that I was a fan, he could see it in my face. Sonic Youth, Nick Cave, Beefheart, Yo La Tengo, Superchunk, 13th Floor Elevators, GBV, classic Flaming Lips, Miles when he got psychedelic, Pavement, Beck, R.E.M. when they were great, the Jesus and Mary Chain, early Sub Pop Compilations. It was a who’s who of the formative years of indie, and all the classic psychedelic stuff that I was missing.

Psychedelic had always been a point for me. I was straight edge for basically all of High School. Worshiping at the alter of Dischord, and lots more embarrassing punk rock things that I don’t care to mention. Think Warped Tour. As vain and silly and predictable as it was: crusty Dreadlocks, safety pin through my ear, band t-shirts, unnecessary patches, duct tape on my Chucks, it was my rebellion. Yes dad shaved off his early 70s hair, and bought a leather jacket at a flea market outside USC in 1978. Yes he saw the Germs. But this was my rebellion because that hair has since grown back. Because of classic rock radio playlists filled with Santana. Because of Dave Mathews band and suburban trustafarians in khaki cargo shorts and hemp necklaces.

It took me until my third year of college to come to terms my roots. I partly blame Freaks and Geeks, for the episode where Lindsey blows off math camp to follow the Dead. I also blame the sale on LPs at the local record store that allowed me to buy ‘Working Man’s Dead’ and ‘American Beauty’ for less than 5 bucks each. Blaming other people, other sources is easy, but I always knew that this was there. Somewhere way down, I was waiting for it, for a way that it could be okay. It came slow. I used to play both of those records softly when I first got them. So my house mates wouldn’t hear, wouldn’t suspect anything. When I was driving myself in my red Subaru station wagon, with all the windows down. That’s when I didn’t have to be ashamed. When I could sing along. I mean, there are limits, I’ve only made it through my inherited and heavily worn LP copy of ‘Europe 72’ once. But put on any of the in-studio classics like ‘Box of Rain’ or ‘Uncle John’s band’ and I know all the words.

It took me a really long time to get through all 300 tapes, because I pretty much only listened to them in that red Subaru station wagon. The year after I graduated I was working cleaning rooms at a bed and breakfast. Commuting and listening to a new tape for me, Pink Floyd on side A, and Hawkwind on side B. I could excuse the Hawkind because of a college professor I had. He wore a different band shirt everyday, had grey hair longer than my dad, almost all the way down his back. Could talk you ear off about Lemmy, and not about the mole on his face or his sideburns, but about his importance as a musician, his role in the New Wave of British Heavy Metal. The 16 year old inside of me squirmed at the thought of Pink Floyd. I could hear the cash register sound from ‘Money,’ and remember a long boring night where I was nowhere near high enough to believe that Dark Side of the Oz actually works. But I gave it a chance, and I have to say that I was pleased, not overwhelmed at first. But I could see the appeal of Syd Barrett. Understand those articles that I’d read defending the legacy of the early incarnation of the group. I could see where the Television Personalities were coming from. This was ‘Piper at the Gates of Dawn,’ not ‘Darkside of the Moon.’ There was no lazer light show. No flying monkeys. Just the sound of overwhelming influence. I could hear so many of my heroes in this, that made it okay, made me more comfortable even though I was alone. And then I got to ‘Bike,’ the last song on the album. About a minute or so in, I almost hit a tree. Almost ran a light, and hit a tree.

“I know a mouse, and he hasn’t got a house/ I don’t know why I call him Gerald/ He’s getting rather old, but he’s a good mouse.” Sings Barret in one of the last verses. That day at Staples came back clearer than ever. I thought of Ryan; the same guy who really got me into punk rock, who had a hardcore band, even a spiked Mohawk for awhile, getting stoned while listening to Pink Floyd. It was okay. Everything that I had worried about, been insecure about. I almost wore out the same tape the year I lived in Chicago. It lived in my Walkman for months at a time. Carrying me on other commutes, or trips to nowhere. Bike rides to the other side of town in inches of snow. Every time I found something new, a riff that drew me in, a lyric, the way Barrett sometimes totally misses notes. It was all there and I was afraid to find it for so long.